Question

Ajutoor!
"1.Rezolvati in Q: a)2\3x+1\6=0; b)3\4x-1,5=0; c)3\5x-1\2=5\10; d)1\2x+5\6==1\3x; e)2\3x-5\3=x-1\3."
"2.Rezolvati in Q ecuatiile: a)2(x+1\2)+5=1\2 b)1\2(2x-6)-5\4=3\2; c)0,(3)x-1,(2)x+0,25=2,5 d)3x+2(x+1\4)=-9."

Answer 1

1a)2/3x+1/6=0
2/3x=-1/6
facem produsul mezilor si extremilor
2·6=(-1)·3x
12=-3x
3x=-12  
x=-12/3
x=-4
S={-4}

b)3/4x-1,5=0
3/4x=1,5
3/4x=15/10
3·10=15·4x
30=60x
60x=30
x=30/60
x=1/2=0,5
S={0,5}

c)3/5x-1/2=5/10
3/5x-1/2=1/2
3/5x=1/2+1/2
3/5x=2/2
3/5x=1
3·1=5x
5x=3
x=3/5=0,6
S={0,6}

d)1/2x+5/6=1/3x
1/2x-1/3x=-5/6
(3-2)/6x=-5/6
1/6x=-5/6
1·6=(-5)·6x
6=-30x
30x=-6
x=-6/30
x=-1/5=-0,2
S={-0,2}

e)2/3x-5/3=x-1/3
2/3x-x=5/3-1/3
(2-3x)/3x=4/3          :3
(2-3x)/x=4
2-3x=4x
-3x-4x=-2
-7x=-2   inmultim -1
x=2/7

2)a)2(x+1/2)+5=1/2
2x+2/2+5=1/2
2x+1+5=1/2
2x+6=1/2
2x=1/2-6
2x=(1-12)/2
2x=-11/2
2x·2=-11
4x=-11
x=-11/4

b)1/2(2x-6)-5/4=3/2
2x/2-6/2-5/4=3/2
x-3-5/4=3/2
x=3/2+5/4+3
x=(6+5+12)/4
x=33/4

c)0,(3)x-1,(2)x+0,25=2,5
0,(3)=3/9=1/3
1,(2)=(12-1)/9=11/9
0,25=25/100=1/4
2,5=25/10=5/2
x/3-11x/9+1/4=5/2
x/3-11x/9=5/2-1/4
(3x-11x)/9=(10-1)/4
-8x/9=9/4
-8x·4=9·9     inmultim -1
8x=-81
x=-81/8=-10,15

d)3x+2(x+1/4)=-9
3x+2x+2/4=-9
5x=-9-2/4
5x=-9-1/2
5x=(-18-1)/2
5x=-19/2
5x·2=-19
10x=-19
x=-19/10
x=-1,9